1. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 1 Fluctuation Studies at STAR Supriya Das* (for STAR Collaboration) Variable Energy Cyclotron Center, Kolkata, India * Present address : Gesellschaft für Schwerionenforschung mbH (GSI) Darmstadt, Germany

2. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 2 Tracking Detectors: TPC, FTPC, SVT Calorimeters: BEMC, EEMC, ZDC Trigger Detectors: CTB, BBC, MWPC Photon Detector: PMD Others: TOF, FPD Goal : to track the hadrons (and photons) in each collision Solenoidal Tracker At RHIC

3. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 3 o Au + Au @ s NN 1/2 = 20, 62, 130, 200 GeV  TPC data with |  | < 1.0, -  <  <    PID from TPC dE/dx  Collision centrality measured by charged particle multiplicity in |  |<0.5 o Centrality slices 0-5%, 5-10%, 10-20 %, … o Use Glauber MC model to estimate number of participants. Features of STAR data (shown in this talk) M. Anderson et al. for STAR Collaboration, NIMA499 (2003)

4. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 4 Fluctuation Analyses from STAR so far Published papers :  Net Charge / Multiplicity fluctuation : PRC 68 (2003) 044905 PLB 634 (2006) 347  Mean p t fluctuation / correlation : PRC 71 (2005) 064906 PRC 72 (2005) 044902 J. Phys G 32 (2006) L37  Balance function : PRL 90 (2003) 172301 Submitted to arXive :  Mean p t fluctuation / correlation: nucl-ex/0408012 nucl-ex/0605022 Many interesting presentations by others on these topics Recent ongoing analyses within the working group: Charge fluctuation (energy dependence, higher moments) Balance function (mass dependence) Long range correlation Event by event K/ ratio

5. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 5 PRC 71 (2005) 064906 Mean p t fluctuation  distribution Deviations from statistical reference Excess in charge independent fluctuation - varies smoothly and monotonically with centrality RHIC events are not fully equilibrated – even for low pt and most central events No evidence of critical fluctuation Results for hadrons for p t < 2GeV/c CI CD

6. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 6 p t correlation (energy dependence)  Non-zero pt correlations in Au+Au collisions from 20 to 200 A Gev  decreases with increasing centrality  dN/d p t:n shows similar behavior as earlier  HIJING shows little or no centrality dependence  Saturation attributed to onset of thermalization or jet suppression PRC 72 (2005) 044902

7. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 7 p t correlation (energy dependence) PRC 72 (2005) 044902  Scaled value of correlation show a little or no dependence on incident energy.  HIJING calculations under predict the data.

8. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 8 p t angular correlation (scale dependence)  p t variance difference increases with increasing collision energy.  Same side peak and away-side ridge in autocorrelation attributed to minijets. nucl-ex/0605022

9. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 9 p t angular correlation (scale dependence)  p t variance difference is centrality dependent  saturation in energy dependence for peripheral collisions Rapid rise within  < 0.2 SSC Slow linear rise after that LSC --- Scale dependence

10. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 10 p t angular correlation (scale dependence) p t variance difference increases with increasing collision energy

11. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 11 p t correlation on ,  Autocorrelations after subtracting monopole, dipole and quadrupole components Au + Au @ 200 GeV Structures attributed to minijets J. Phys G 32 (2006) L37 Scale dependence of variance difference and corresponding autocorrelations variance difference auto-correlation

12. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 12 confined: few d.o.f. deconfined: many d.o.f. Prediction: A drastic decrease in the EbyE fluctuations of net charge in local phase space regions in the deconfined QGP phase compared to that of the confined case hadronic gas. QGP:4 and pion gas: 1-2 Jeon, Koch: PRL (2000) 2076 Asakawa, Heinz & Muller: PRL (2000) 2072 Evolution of fluctuation Shuryak & Stephanov: PR C63 (2001) 064903 Heiselberg & Jackson: PR C63 (2001) 064904 Mohanty, Alam & Nayak: PR C67 (2003) 024904 Net Charge fluctuation (motivation) Charged multiplicity: n ch = n + + n – Net charge: Q = n + - n – Charge ratio: R = n + / n - (1) v(Q)  Var(Q)/ (for stochastic emission, v(Q) = 1) (2) v(R)  Var(R) * (for stochastic emission, v(R) = 4) (3)  (Q)  dynamic (5)Moments of Net charge distributions

13. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 13 Net Charge fluctuation Au+Au @ 130 GeV PRC 68 (2003) 044905 Charge conservation limit Resonance gas Charge conservation limit  Fluctuation for inclusive non-identified charge particles exceed by factor of 2 compared to charge conservation limit  Results agree with expectation based on measurement from p+p collisions at ISR  Two particle correlation may be modified in central collisions relative to the peripheral collisions  Fluctuation measure closer to the prediction with resonance gas  Pions show little larger fluctuation compared to inclusive measurement  Kaons and protons show 2 to 4 times the value of fluctuation compared to inclusive measurement

14. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 14 Net Charge fluctuation (energy dependence) C. Pruneau - nucl-ex/0401016 C. Pruneau QM 05 PHENIX |  |<0.35,  =  /2 CERES 2.0<  <2.9 STAR: 5% Central Au+Au Dynamical net charge fluctuation are invariant of beam energies starting from top SPS onwards.

15. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 15 Moments of net charge distributions (motivation) Lattice calculations Ejiri, Karsch and Redlich: hep-ph/0510126 Gavai, Gupta: hep-lat/0510044 Net charge Isospin Strangeness  Interesting structure close to T=T C Is it possible to make precise measurement of higher moments of net charge? bins in centrality bins in p T Calculation of Non-linear susceptibilities (higher order derivatives of pressure with respect to chemical potentials): 2 nd moment 4 th moment 6 th moment (similar to kurtosis)

16. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 16 Net charge (Q) distributions MEAN of Q distributions /N part Q (net charge) Q distributions for AuAu 200GeV at 4 different centralities and 6 bins in p T low p T high p T /N part is independent of centrality.T. Nayak – SQM ‘06

17. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 17 Variance and kurtosis of net charge distributions AuAu 200GeV (Q) with p T binned  (Q) is low at low p T and increases with increase of p T. Could be an effect of more resonance production at low p T.  First analysis of the 4 th moment of net charge distribution is performed. Detailed comparison in terms of lattice calculations is expected soon. Centrality & p T Kurtosis ( 4 th moment ) T. Nayak – SQM ‘06

18. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 18 Opposite charged particles are created at the same location of space–time. Charge–anticharge particles created earlier (early stage hadronization) get further separated in rapidity. Particle pairs that were created later (late stage hadronization) are correlated at small Δy. The Balance Function quantifies the degree of this separation and relates it with the time of hadronization. Bass-Danielewicz-Pratt, PRL 85, 2000 D. Drijard et al, NP B(155), 1979 Early Hadronization  Large  Late Hadronization  Small  Z=0 Balance function (motivation)

19. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 19 Balance function PRL 90 (2003) 172301  Width of balance function is narrower for more central collision.  HIJING matches with data only for peripheral collisions. Au+Au @ 130 GeV Inclusive charged pairs Identified pions

20. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 20 Heavier particles are characterized by narrower bf distributions: Balance function (mass dependence) Gary Westfall, J.Phys.G30, S345-S349 (2004) The balance function width for pions get narrower with increasing centrality, remains constant for kaons. HIJING reproduces results for kaons, but not for pions. The ratio of widths of pions to kaons is consistent with delayed hadronization picture. 1.3-1.4

21. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 21 Long-range multiplicity correlations  Study of correlations among particles produced in different rapidity regions.  The long-range correlations are expected to be much stronger in p-A and A-A, compared to p-p at the same energy. Terence J Tarnowsky Nuclear Dynamics, San Diego March 2006 nucl-ex/0606018 STAR: forward region of 0.8<  <1.0 & backward of -1.0<  <-0.8. Increase in correlation strength observed for central collisions compared to peripheral for Au+Au collisions at 200GeV. Correlation strength:

22. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 22 nucl-ex/0606018 Long-range multiplicity correlations For central collision, long range correlation is less than PSM calculation

23. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 23 Strangeness fluctuation (motivation) S. Afanasiev for NA49 PRL 86 (2001) C. Roland QM 2004  Dynamical fluctuation is positive  Amount of fluctuation decreases with increase in collision energy.  Data disagree with UrQMD model

24. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 24 [ Data not corrected for efficiency] Strangeness fluctuation : K/  distribution S. D. : SQM’06 Symposium

25. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 25 Strangeness fluctuation (energy and centrality dependence) S. D. : SQM’06 Symposium Fluctuation in K/  decreases with increasing energy till the top SPS energy and remains flat above it. The amount of fluctuation decreases with increasing centrality and is similar for 62GeV as well as 200GeV AuAu collisions.  rms/mean  dyn = sqrt(  data 2 –  mixed 2 )

26. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 26 Summary  STAR has the capability to study the event by event fluctuation for many different observables.  Mean p t fluctuation results show non-zero fluctuation which scales with centrality.  Mean p t analysis in finer (,) subspace shows interesting structures which could be attributed to production of minijets.  Net charge fluctuation is greater than predicted value from charge conservation conjecture but closer to resonance gas picture.  Dynamical net charge fluctuation is essentially flat for energies more that top SPS.  Results from higher moments of net charge are promising, but needs more work.  Balance function results support delayed hadronization picture.  Long range multiplicity correlation reduces (compared to model calculation) in central collisions.  Event by event fluctuation in K/ratio is positive and centrality dependent but show no dependence on collision energy at RHIC.

27. Supriya DasCorrelation and Fluctuation in Relativistic Nuclear Collisions - Florence, July 2006 27 Outlook STAR has a shining future in the proposed low energy scan at RHIC With wider momentum range and K,  separation, it will play a key role in strangeness fluctuation study STAR will also give more insights in the energy dependence of Balance function at lower energies

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